If parliament fails to establish the tribunal itself it will be automatically set up by the legally binding resolution.
The issue has been at the core of an acute political crisis in Lebanon that has paralysed the government for months.
Berri had refused to call parliament to vote on UN plans for the court because he contests the legitimacy of the Beirut government led by Fouad Siniora, the prime minister.
The Security Council vote was 10-0 with five nations abstaining - Russia, China, South Africa, Indonesia and Qatar.
The council adopted the resolution under Chapter Seven of the UN charter, which is invoked in cases of threats to international peace and security.
Bashar Jaafari, Syria's ambassador to the UN, said on Wednesday: "Definitely this is something that goes against the interests of the Lebanese people and Lebanon as a whole."
|Al-Hariri's supporters welcomed the resolution |
with fireworks and celebratory gunfire [AFP]
A UN inquiry has implicated senior Syrian figures and their Lebanese accomplices in the assassination.
The government in Damascus has rejected the accusations and its allies in the Lebanese opposition say the tribunal will be used as political tool by the US.
The Lebanese opposition, led by the Shia group Hezbollah, has vowed it will never accept the tribunal and blocked government efforts to win parliament's endorsement for the project.
A Hezbollah statement said the council vote had "opened the door to international interference and hegemony" in Lebanon and that the resolution had breached national and international law.
Saad al-Hariri, the son and political heir of the former prime minister, and his allies have accused Syria of being the bombing which killed al-Hariri and 22 others in Beirut.
On Thursday, he said the tribunal would end the impunity that political assassins have enjoyed in Lebanon for four decades.
"How could the tribunal affect the security of Lebanon? How could punishing the people who killed Rafiq al-Hariri... affect the security of Lebanon?" he asked.
"If Lebanon is going to be unstable it is the doing of those who say that Lebanon is going to be unstable.
"They [the Syrians] won't be able to destabilise us because they tried before and they have failed."
Hariri said opposition leaders, including Berri and Hezbollah's Sayyed Hassan Nasrallah, were being threatened by Syria and coerced into opposing the tribunal.
Meanwhile, the road in Beirut where al-Hariri was killed by a massive suicide truck bomb has finally been reopened after more than 800 days.
The 300-metre-long stretch of road had been closed while UN investigators looked for evidence.